Finite Group Databasebeta

← #28389499

Subgroups — #28389499

Order 14464.

316 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299224C211yesmaximal, characteristic, complemented
2#20298751C212yesmaximal, complemented
3#20298507C211yesmaximal, characteristic
4#20298336C212yesmaximal, complemented
5#323×C113C211yesmaximal, characteristic, complemented
6C22×D452C2211yescharacteristic
7C22×C22⋊D113—21no—
8C2×#14268636—22no—
9#16813601—21no—
10#16813601C2212yes—
11#16813599—22no—
12#16813599—22no—
13C2×C22⋊Dic113—21no—
14C2×#14268624—21no—
15#16813544—22no—
16#16813529C2211yescharacteristic
17C2×C22⋊C4×C113C2211yescharacteristic
18C22⋊C8×C113C2212yes—
19C23×D113—21no—
20C2×Dic226—21no—
21C2×Dic226D412yescomplemented
22C2×D452—22no—
23C2×D452—42no—
24C2×C22⋊D113—42no—
25C2×C22⋊D113—42no—
26C2×C22⋊D113—42no—
27C22×Dic113—21no—
28C22×Dic113—21no—
29C22×Dic113—21no—
30#14268636—44no—
31C4⋊Dic113—21no—
32C4⋊Dic113D412yescomplemented
33#14268626—22no—
34#14268626—22no—
35C22⋊Dic113—22no—
36C22⋊Dic113—22no—
37#14268624—42no—
38C24×C113D411yescharacteristic
39C22×C4×C113D411yescharacteristic
40C22×C4×C113C2311yescharacteristic
41C2×C8×C113—22no—
42C22⋊C4×C113—22no—
43C23×C113—21no—
44C23×C113—21no—
45C23×C113—41no—
46C23×C113—41no—
47C23×C113SD1612yescomplemented
48C23×C113C2×D411yescharacteristic
49C22×D113—22no—
50C22×D113—41no—
51C22×D113—41no—
52C22×D113—41no—
53C22×D113—41no—
54C22×D113—41no—
55C22×D113—41no—
56C2×C4×C113—21no—
57C2×C4×C113—41no—
58C2×C4×C113—41no—
59C2×C4×C113C2×D412yes—
60C22⋊D113—48no—
61C2×Dic113—22no—
62C2×Dic113—22no—
63C2×Dic113—22no—
64C2×Dic113—41no—
65C2×Dic113—41no—
66C2×Dic113—81no—
67C2×Dic113—81no—
68D452—24no—
69D452—42no—
70Dic226—42no—
71Dic226—81no—
72C8×C113—42no—
73C22×C113—21no—
74C22×C113—21no—
75C22×C113—22no—
76C22×C113—42no—
77C22×C113—41no—
78C22×C113—41no—
79C22×C113—81no—
80C22×C113#12011yescharacteristic
81C22×C113C2×SD1611yescharacteristic
82C22×C113#13711yescharacteristic
83C2×D113—42no—
84C2×D113—42no—
85C2×D113—42no—
86C2×D113—81no—
87C2×D113—81no—
88C2×D113—81no—
89C2×D113—81no—
90C4×C113—22no—
91C4×C113—41no—
92Dic113—42no—
93Dic113—42no—
94Dic113—42no—
95C2×C113—21no—
96C2×C113—21no—
97C2×C113—42no—
98C2×C113#44811yescharacteristic
99C2×C113#45311yescharacteristic
100C2×C113B(4,𝔽2)11yescharacteristic
101D113—82no—
102#1596—1131nomaximal, Sylow
103C113#159611yescharacteristic, complemented, Sylow
104#543—1131no—
105#450—1132no—
106#392—1131no—
107#328—1132no—
108#323D11311yescharacteristic, complemented
109C22×D4—1131no—
110C22×D4—2261no—
111C2×SD16—2262no—
112C22⋊Q8—1132no—
113C22⋊Q8—2262no—
114C22⋊Q8—2262no—
115C22⋊Q8—2261no—
116C2×C22⋊C4—2261no—
117C2×C22⋊C4—2261no—
118C2×C22⋊C4C2×D11311yescharacteristic
119#102—2262no—
120C22⋊C8C2×D11312yes—
121#95—1131no—
122C24—2261no—
123C24D45211yescharacteristic
124C2×Q8—1132no—
125C2×Q8—2261no—
126C2×D4—4522no—
127C2×D4—4522no—
128C2×D4—4522no—
129C2×D4—4522no—
130C2×D4—2262no—
131C22×C4—2261no—
132C22×C4—2261no—
133C22×C4—2261no—
134C22×C4D45211yescharacteristic
135C22×C4C22×D11311yescharacteristic
136SD16—4524no—
137C2×C8—22no—
138C4⋊C4—1132no—
139C4⋊C4—2262no—
140C4⋊C4—2261no—
141C4⋊C4—2262no—
142C22⋊C4—22no—
143C22⋊C4—4522no—
144C22⋊C4—2262no—
145C22⋊C4—2262no—
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—4521no—
151C23—4521no—
152C23—4521no—
153C23—4521no—
154C23—4521no—
155C23—4521no—
156C23—2262no—
157C23#1426863612yescomplemented
158C23C2×D45211yescharacteristic
159Q8—9041no—
160Q8—4522no—
161D4—4522no—
162D4—4528no—
163D4—2264no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—9041no—
168C2×C4—9041no—
169C2×C4—4521no—
170C2×C4—4521no—
171C2×C4—2262no—
172C2×C4—2262no—
173C2×C4—2262no—
174C2×C4D4×D11312yes—
175C8—42no—
176C22—21no—
177C22—21no—
178C22—22no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—9041no—
184C22—9041no—
185C22—9041no—
186C22—9041no—
187C22—4522no—
188C22—4522no—
189C22—4522no—
190C22#1681359211yescharacteristic
191C22C2×#1426863611yescharacteristic
192C22#1681365511yescharacteristic
193C4—22no—
194C4—41no—
195C4—4522no—
196C4—4522no—
197C4—4522no—
198C2—21no—
199C2—21no—
200C2—42no—
201C2—9042no—
202C2#2029873911yescharacteristic
203C2#2029876811yescharacteristic
204C2#2029878611yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#323×C113C2
socleC22×C113#120
prime radical#20298507C2
hypercenter#323D113
hypocenterC113#1596
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20299224C2semidirect
2. #20298751C2semidirect
4. #20298336C2semidirect
5. #323×C113C2semidirect
21. C2×Dic226D4semidirect
32. C4⋊Dic113D4semidirect
47. C23×C113SD16semidirect
103. C113#1596semidirect
108. #323D113semidirect
157. C23#14268636semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202992242
#202987512
#202985072
#202983362
#323×C1132
#1596113